Jacob Marschak

Optimal inventory policy

WE ipropose to outline a method for deriving optimal rules of inventory policy for finished goods. The problem of inventories exists not only for business enterprises but also for nonprofit agencies such as governmental establishments and their various branches. Moreover, the concept of inventories can be generalized so as to include not only goods but also disposable reserves of manpower as well as various stand-by devices. Also, while inventories of finished goods present the simplest problem, the concept can be extended to goods which can be transformed, at a cost, into one or more kinds of finished goods if and when

Random Orderings and Stochastic Theories of Response

In interpreting human behavior there is a need to substitute ‘stochastic consistency of choices’ for ‘absolute consistency of choices’. The latter is usually assumed in economic theory, but is not well supported by experience. It is, in fact, not assumed in empirical econometrics and psychology.

Rational Behavior, Uncertain Prospects, and Measurable Utility (1950)

After introducing some basic concepts and three postulates on rational choice, it is proposed to show that if the economists’ theory of assets is completed by a fourth postulate on rational choice, then utility can be defined as a quantity whose mathematical expectation is maximized by the rational man. In this sense, utility is ‘measurable’ and ‘manageable’. These results are inspired by von Neumann’s and Morgenstern’s discussion of utility in Theory of Games and Economic Behavior; an attempt is made to sketch some relations between their approach and the present one, It is shown in conclusion that while gambling is compatible with the four postulates, the ‘love of danger’ is not: and a property of the maximum mathematical expectation of utility is conjectured.

ECONOMIC COMPARABILITY OF INFORMATION SYSTEMS.

An information system is a set of potential messages to be received by the decision maker. It is characterized by the statistical relation of the messages to the payoff-relevant events, and also by the message cost.1 Neglecting this cost, the (gross) value of an information system for a given user is the (gross) payoff that he would obtain, on the average, if he would respond to each message by the most appropriate decision. Thus (gross) information value depends not only on the statistical relation between messages and events but also on the payoff function. The latter expresses the user’s ‘tastes’ and ‘technology’. The ordering of statistically defined information systems by their values is therefore at most a partial one. This contrasts with the complete ordering of information systems (channels) by their equivocation (a statistical parameter used in the classical information theory that disregards variation of payoff functions from user to user).

Economics of Information Systems

Abstract n an information-processing chain, only the initial inputs (“environment”) and the terminal outputs (“actions”) affect directly the benefit to the user who maximizes its expected excess over cost. All intermediate flows (“symbols”) affect directly only costs and delays. Delays affect benefit non-additively, through “impatience” and, possibly, “obsolescence.” Traditionally, statistical theory disregards delays, and communication theory treats them as costs. A more complete, unifying approach is proposed, and it is asked whether convexity conditions (e.g., “decreasing marginal returns”) required for competitive market equilibrium are satisfied.

Money and the Theory of Assets

There has been until recently little connection between what is usually taught as Monetary Theory and the General Theory of Prices (or Value). Furthermore, there is little connection between the two compartments of Monetary Theory: the Theory of the ‘Equation of Exchange’ with its underlying concepts, Price Level, Velocity of Circulation, Real Income, etc., on the one hand and, on the other, the Theory of Credit and Banking. The Babylonian lack of common language between the two compartments of Monetary Theory is well illustrated by the fact that, while ‘Exchange Value of Money’ (Wicksell, Robertson) is defined as the reciprocal of the Price Level, the term Price of Money is often used to designate interest rates on short loans — although usually economists agree to use Exchange Value of a thing and Price of a thing as equivalent terms. In neither of the two compartments of Monetary Theory is much use made of the fundamentals of economic theory. The Price Level is treated as if it had nothing to do with prices. The velocity of circulation has been, thanks to the Cambridge School, associated with cash holdings instead of being left in the air; but the next step, to treat cash holdings on the same lines on which holdings of any other Stocks are treated in the General Theory of Prices, has been made by few economists only, of whom Dr. Hicks is the most outstanding.1 Similarly, the Interest Rate of the treatises on Banking and Trade Cycle seems to be ashamed of any connection with its less adventurous and ‘dynamic’ but more scholarly relation, the Interest Rate of the marginal productivity theory: the parentage is casually mentioned, if at all, in a few hurried phrases only.

Personal probabilities of probabilities

By definition, the subjective probability distribution of a random event is revealed by the (‘rational’) subjects choice between bets — a view expressed by F. Ramsey, B. De Finetti, L. J. Savage and traceable to E. Borel and, it can be argued, to T. Bayes. Since hypotheses are not observable events, no bet can be made, and paid off, on a hypothesis. The subjective probability distribution of hypotheses (or of a parameter, as in the current ‘Bayesian’ statistical literature) is therefore a figure of speech, an ‘as if’, justifiable in the limit. Given a long sequence of previous observations, the subjective posterior probabilities of events still to be observed are derived by using a mathematical expression that would approximate the subjective probability distribution of hypotheses, if these could be bet on. This position was taken by most, but not all, respondents to a ‘Round Robin’ initiated by J. Marschak after M. H. De-Groots talk on Stopping Rules presented at the UCLA Interdisciplinary Colloquium on Mathematics in Behavioral Sciences. Other participants: K. Borch, H. Chernoif, R. Dorfman, W. Edwards, T. S. Ferguson, G. Graves, K. Miyasawa, P. Randolph, L. J. Savage, R. Schlaifer, R. L. Winkler. Attention is also drawn to K. Borchs article in this issue.

Role of Liquidity under Complete and Incomplete Information

It is proposed to study how the demand of rationally acting men for a commitment (an asset or a contract) depends on its liquidity under various degrees of available information.

THE PAYOFF-RELEVANT DESCRIPTION OF STATES AND ACTS.

Typically, a problem in information economics consists of choosing simultaneously an optimal pair: (1) an information channel producing messages, and (2) a decision rule associating each message with an act. The givens of the problem are: the probability distribution on the states of the world, and the utility yielded by each combination of act and state, taking account of message costs.

Money Illusion and Demand Analysis

In recent months, the present writer has had the opportunity of listening to discussions of practical men on the question: To reduce the demand for consumers’ goods, which of two measures is more effective, a tax on incomes at the source (withholding tax) or a sales-tax? I have heard contradictory opinions, all based on purported knowledge of ‘the worker’s’ or ‘the housewife’s’ psychology. Some said that a thinner pay envelope would duly impress the would-be spender; others endowed the price tag with stronger deterrent powers.